%I A112844
%S A112844 1,2,5,13,34,89,89,193,185,410,482,1444,2018,6362,8461,19885,22861,
%T A112844 51125,59792,146749,195749,529114,730465,1907545,2350177,5638489,
%U A112844 6692337,16167545,20091490,51762100,67753160,178151440,229118152
%N A112844 Small-number statistic from the enumeration of domino tilings of a 9-pillow 
               of order n.
%C A112844 A 9-pillow is a generalized Aztec pillow. The 9-pillow of order n is 
               a rotationally-symmetric region. It has a 2 X 2n central band of 
               squares and then steps up from this band with steps of 9 horizontal 
               squares to every 1 vertical square and steps down with steps of 1 
               horizontal square to every 1 vertical square.
%C A112844 Plotting A112844(n+2)/A112844(n) gives an intriguing damped sine curve.
%D A112844 C. Hanusa (2005). A Gessel-Viennot-Type Method for Cycle Systems with 
               Applications to Aztec Pillows. PhD Thesis. University of Washington, 
               Seattle, USA.
%e A112844 The number of domino tilings of the 9-pillow of order 8 is 9065=7^2*185. 
               A112844(n)=185.
%Y A112844 A112842 breaks down as A112843^2 times A112844, where A112844 is not 
               necessarily square-free.
%Y A112844 3-pillows: A112833-A112835; 5-pillows: A112836-A112838; 7-pillows: A112839-A112841.
%Y A112844 Sequence in context: A122024 A027931 A103142 this_sequence A027933 A141448 
               A011783
%Y A112844 Adjacent sequences: A112841 A112842 A112843 this_sequence A112845 A112846 
               A112847
%K A112844 easy,nonn
%O A112844 0,2
%A A112844 Christopher Hanusa (chanusa(AT)math.binghamton.edu), Sep 21 2005